Qualitative analysis of phase--portrait for a class of planar vector fields via the comparison method

Abstract

The phase--portrait of the second order differential equation: $$\ddot{x}+\sum _{l=0}^n{f}_l(x){\dot{x}}^l=0,$$ is studied. Some results concerning existence, non--existence and uniqueness of limit cycles are presented. Among these, a generalization of the classical Massera uniqueness result is proved.

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